.5x^2+9x+3.2=0

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Solution for .5x^2+9x+3.2=0 equation: 


Simplifying
0.5x2 + 9x + 3.2 = 0

Reorder the terms:
3.2 + 9x + 0.5x2 = 0

Solving
3.2 + 9x + 0.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.5 the coefficient of the squared term: 

Divide each side by '0.5'.
6.4 + 18x + x2 = 0

Move the constant term to the right:

Add '-6.4' to each side of the equation.
6.4 + 18x + -6.4 + x2 = 0 + -6.4

Reorder the terms:
6.4 + -6.4 + 18x + x2 = 0 + -6.4

Combine like terms: 6.4 + -6.4 = 0.0
0.0 + 18x + x2 = 0 + -6.4
18x + x2 = 0 + -6.4

Combine like terms: 0 + -6.4 = -6.4
18x + x2 = -6.4

The x term is 18x.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18x + 81 + x2 = -6.4 + 81

Reorder the terms:
81 + 18x + x2 = -6.4 + 81

Combine like terms: -6.4 + 81 = 74.6
81 + 18x + x2 = 74.6

Factor a perfect square on the left side:
(x + 9)(x + 9) = 74.6

Calculate the square root of the right side: 8.637129153

Break this problem into two subproblems by setting 
(x + 9) equal to 8.637129153 and -8.637129153.


Subproblem 1
x + 9 = 8.637129153

Simplifying
x + 9 = 8.637129153

Reorder the terms:
9 + x = 8.637129153

Solving
9 + x = 8.637129153

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + x = 8.637129153 + -9

Combine like terms: 9 + -9 = 0
0 + x = 8.637129153 + -9
x = 8.637129153 + -9

Combine like terms: 8.637129153 + -9 = -0.362870847
x = -0.362870847

Simplifying
x = -0.362870847


Subproblem 2
x + 9 = -8.637129153

Simplifying
x + 9 = -8.637129153

Reorder the terms:
9 + x = -8.637129153

Solving
9 + x = -8.637129153

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + x = -8.637129153 + -9

Combine like terms: 9 + -9 = 0
0 + x = -8.637129153 + -9
x = -8.637129153 + -9

Combine like terms: -8.637129153 + -9 = -17.637129153
x = -17.637129153

Simplifying
x = -17.637129153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.362870847, -17.637129153}

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